1. Field of the Invention
The present invention relates to a method for modelling low or high compressibility fluid flows in a multilayer porous medium crossed by a network of fractures of given geometry, unevenly distributed in the medium, some of the fractures communicating with one another.
2. Description of the Prior Art
a) During oil well testing, the flow rate conditions imposed on the well cause the oil contained in the reservoir to flow towards the well. It is a single-phase (the only mobile phase is the oil) and a low compressibility flow.
For any elementary volume of the reservoir, the pressure of the oil contained in this volume is governed by the following equation (gravity is not taken into account):
                              ϕ          ·                      C            T                    ·                                    ∂              P                                      ∂              t                                      =                              div            ⁡                          (                                                K                  μ                                ·                                  ∇                  P                                            )                                +          Q                                    (        1        )            where:Φ: represents the pore volume,CT, the total compressibility (fluid+rock),K, the permeability of the rock,μ, the viscosity of the fluid,Q, the incoming flow,P, the pressure unknown.
b) During gas well testing, the only mobile phase is the gas and it is highly compressible. For any elementary volume of the reservoir, the pressure of the gas contained in this volume is governed by the following equation:
                              ϕ          ·                      C            T                    ·                                    ∂              ψ                                      ∂              t                                      =                              div            ⁡                          (                                                K                  μ                                ·                                  ∇                  ψ                                            )                                +                                                    2                ⁢                p                            μZ                        ⁢            Q                                              (        1        )            where:Φ: represents the pore volume,CT, the total compressibility (fluid+rock),K, the permeability of the rock,μ, the viscosity of the fluid,Z, the gas compressibility factor,Q, the incoming flow, andψ, a pseudopressure function defined by
      ψ    =          2      ⁢                        ∫                      p            0                    p                ⁢                              p                          μ              ⁢                                                          ⁢              Z                                ⁢                                          ⁢                      ⅆ            p                                ,where p is the pressure of the fluid.
The viscosity and the compressibility factor of the gas vary as a function of the pressure and they are given for a certain number of values in a table referred to as PVT table (Pressure Volume Temperature). From this table, the pseudopressure function defined above can be deduced and the gas compressibility deduced from the equation of state. The PVT table is thus a table with 5 columns (pressure, pseudopressure, viscosity, compressibility factor and gas compressibility) from which, at a given pressure, the corresponding pseudopressure, viscosity and compressibility can be obtained by linear interpolation (conversely, the other 4 data can be obtained by interpolation from a pseudopressure).
The incoming flow Q is zero everywhere, except in the places where the well communicates with the reservoir.
In order to simulate a well test, whatever the medium, this equation has to be solved in space and in time. Definition of the reservoir (grid pattern) is therefore performed and a solution to the problem is finding the pressures of the grid cells in the course of time, itself defined in a certain number of time intervals.
There are known single-phase flow modelling tools, which are however not applied to the real complex geologic medium but to a homogenized representation, according to the reservoir model called double-medium model described for example by Warren and Root in “The Behavior of Naturally Fractured Reservoirs”, SPE Journal, September 1963. Any elementary volume of the fractured reservoir is thus modelled in the form of a set of identical parallelepipedic blocks limited by an orthogonal system of continuous uniform fractures oriented in the direction of one of the three main directions of flow (model referred to as “sugar box” model). The fluid flow on the reservoir scale occurs mainly through the fractured medium, and fluid exchanges take place locally between the fractures and the matrix blocks. This representation, which does not reproduce the complexity of the fracture network in a reservoir, is however effective but at the level of a reservoir grid cell whose typical dimensions are 100 m×100 m.
It is however much preferable for reservoir engineers to have a flow simulator based on a “real” geologic model of the medium instead of an equivalent homogeneous model, so as to:
validate the geologic image of the reservoir built by the geologist from all the information gathered on the reservoir fracturation (this validation being performed by comparison with the real well test data),
reliably test the sensitivity of the hydraulic behaviour of the medium to the uncertainties on the geologic image of the fractured medium.
A well-known modelling method finely grids the fracture network and the matrix while making no approximation concerning fluid exchanges between the two media. It is however difficult to implement because the often complex geometry of the spaces between the fractures makes it difficult to grid them and, in any case, the number of grid cells to be processed is often very large. The complexity increases still further with a 3D grid pattern.
Techniques for modelling fractured porous media are described in French patents 2,757,947 and 2,757,957 filed by the assignee.
The former technique relates to determination of the equivalent fracture permeability of a fracture network in an underground multilayer medium from a known representation of this network, allowing systematic connection of fractured reservoir characterization models to double-porosity simulators in order to obtain more realistic modelling of a fractured underground geologic structure.
The second technique relates to simplified modelling of a porous heterogeneous geologic medium (such as a reservoir crossed through by an irregular network of fractures for example) in the form of a transposed or equivalent medium so that the transposed medium is equivalent to the original medium, according to a determined type of physical transfer function (known for the transposed medium).
French patent 2,809,494 filed by the assignee describes a method for simulating fluid flows in a fractured porous geologic medium crossed by a network of conducting objects of defined geometry, but which cannot be homogenized on the scale of each grid cell of the model (large fractures, subseismic faults for example, very permeable sedimentary layers, etc.), wherein the exchanges occurring between the matrix medium and the fracture medium are determined, and for modelling the transmissivities of the various grid cells crossed by each conducting object, so that the resulting transmissivity corresponds to the direct transmissivity along each object. In cases where the conducting objects are very permeable sedimentary layers, the transmissivity between the grid cells crossed by each highly permeable layer is given a value that depends on the dimensions of the grid cells and on the common area of contact between the layers at the junction of the adjacent grid cells. In cases where the conducting objects are fractures, the transmissivity between the grid cells crossed by each fracture is given a transmissivity that depends on the dimensions of the grid cells and on the common area of the fracture at the junction of the adjacent grid cells.
French patent 2,787,219 filed by the assignee describes a method for modelling low compressibility fluid (oil) flows in a fractured multilayer porous medium by accounting for the real geometry of the fracture network and of the local exchanges in the porous matrix and between the porous matrix and the fractures at each node of the network. The fractured medium is defined by a grid pattern and the fracture grid cells are associated with nodes placed either at the fracture intersections or at the fracture ends. Each node is associated with a matrix block or volume, the flows between each fracture grid cell and the associated matrix volume are calculated in a pseudosteady state. In cases where the fracture network is weakly connected, that is the fracture network does not run through all of the considered matrix volume, the direct flows between the matrix volumes through the common edges of the grid cells are also determined. Accounting for the transmissivities between matrix blocks associated with medium discretization nodes allows more realistic simulation of the response of a well to imposed flow rate variations.